The above argument remains valid if the imaginary part of the self-energy has a Dirac \(\delta \)  centered exactly at the Fermi level, as it happens in the NLFL [1]}
where \({\rm Im}\Sigma ^d_{\tau \sigma } = -a\omega ^2 - b\delta (\omega )\) . The generalized Friedel sum rule for the spectral funcion \(\rho _{\tau \sigma }(\omega \rightarrow 0)\) 
(REF ) therefore holds even for the NLFL.
